We introduce an ideal limit of rhombohedral graphene in which interactions spontaneously generate a correlated Chern insulator. Our analysis reveals that this Chern insulator can be understood as a layer-pseudospin skyrmion lattice stabilized by electronic interactions, and that it gives rise to genuine skyrmion lattice physics, complete with dynamics. This dynamical skyrmion lattice naturally leads to experimentally measurable consequences. In particular, we identify new collective excitations corresponding to chiral shape deformations of the skyrmions, and propose a new positively charged quasiparticle, the skyrmion vacancy. These results establish a qualitatively new form of moir'e Chern physics in rhombohedral graphene: an interaction-generated skyrmion lattice whose skyrmions are dynamical low-energy degrees of freedom.